It's still in the early stages but...
In order to prolong he life every few years she has to pass her illness off to another. she has no control over who gets it. She steals what would have been left of their life only getting sick again when they would have dies. And she sees what she stole (when she sleeps) but can not return to the world what she took. She gives the illness to her lover just one of many in her immortal life, he falls sick and dies (some great man that did a lot). While she does not care for him herself she sees the destruction she caused. In present day (but not as advanced)she attempts to reach him to replicate his experiments, but she can't. When she steals another's life she realizes it is the partner of a man with the same genius and sets put to find him. She uses the dreams to find him and to help him with the experiments. He falls ill and she finds the one who gave her the gift/curse to help him as well. If he lived forever than he could help the world so much (she also has fallen in love with him after longing for so long after her the man this one represents.
It's not done yet, it still needs to be expanded.